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  • 1
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 37 (1996), S. 5297-5309 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Supersymmetric quantum mechanics cannot be deformed when the superposition of only a pair of usual bosons and fermions is considered, but it can if nontrivial parabosons and parafermions of the same order p of paraquantization are superposed. We take the simplest case p=2 and exhibit reducibility problems in that context by using Green–Cusson Ansätze following Macfarlane methods. Specific representations of the Lie superalgebra osp (2|2, R) play an interesting role in connection with possible deformations. © 1996 American Institute of Physics.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 3387-3392 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Different choices of matrices characterizing p=2 parafermions are analyzed in connection with the description of relativistic spin-one particles through the Kemmer formulation. The free and interacting cases are considered and the relations between parasupersymmetry and Kemmer theory are enhanced as it is also the case between supersymmetry and Dirac theory. In that way the oscillatorlike context leads to the characterization of pararelativistic oscillators.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 32 (1991), S. 1815-1821 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The spin-orbit coupling supersymmetrization procedure is considered in parasupersymmetric quantum mechanics describing oscillatorlike systems. The superposition of bosonic and parafermionic degrees of freedom is mainly studied in the cases of two and three spatial dimensions but the n-dimensional case is also determined. New Lie superalgebras and Lie parasuperalgebras are pointed out: They differ from those already obtained in connection with the standard procedure of supersymmetrization studied in Part I of this series [J. Beckers and N. Debergh, J. Math. Phys. (square, solid)(square, solid), (square, solid)(square, solid)(square, solid) (1991)].
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 30 (1989), S. 1732-1738 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Generalized coherent states for the one-dimensional harmonic oscillator with maximal symmetry, i.e., admitting the semidirect sum so(2,1) (D'Alembertian) h(2) as the largest invariance Lie algebra pointed out by Niederer are constructed. The normalization of such states as well as their completeness property are determined and discussed. They are also analyzed in the subcontexts of the so(2,1) algebra and of the Heisenberg h(2) algebra. General considerations on Heisenberg relations, on minimal dispersions, and on quantum mechanical entropies are presented in connection with the uncertainty principle.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 36 (1995), S. 641-647 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Supersymmetric three-dimensional Schrödinger equations describing central problems do not lead, in general, to supersymmetric one-dimensional radial equations. Such a context is discussed, in connection with the two main supersymmetrization procedures (with or without spin-orbit coupling terms). The inverse problem is also considered, starting from a supersymmetric radial equation. © 1995 American Institute of Physics.
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 34 (1993), S. 1270-1276 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The energy spectra of the systems corresponding to the superposition of (para) bosons and (para)fermions are analyzed. Such a study is subtended by the exploitation of the positive discrete series of the superalgebra osp(2||2,R) associated with the two relative parabose and parafermi sets of trilinear structure relations. In particular, the spectra corresponding to exact or broken supersymmetry are recovered for specific values of the orders of paraquantization but new ones are also present with their own typical properties.
    Type of Medium: Electronic Resource
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  • 7
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 394-398 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Parabosonic coherent states are illustrated from the displacement operator point of view. Such a construction requires the use of the Green–Cusson Ansätze, a specific representation of parastatistics, leading to color supergroups. A comparison with a previous result is shown through the annihilation operator and the minimum uncertainty contexts. The extension to the parasupersymmetric case is also considered.
    Type of Medium: Electronic Resource
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  • 8
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 32 (1991), S. 1808-1814 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Parasupersymmetric quantum mechanics leads to the construction of new Lie structures that are called Lie parasuperalgebras. They are characterized by double commutation relations between even and odd generators and include as particular substructures the usual Lie superalgebras. Oscillatorlike systems in one spatial dimension are especially exploited in order to put such structures in evidence but n-dimensional extensions are easily determined. These developments in the standard supersymmetrization procedure will be considered first and the spin orbit coupling one will be considered in a subsequent article [J. Beckers and N. Debergh, J. Math. Phys. (square, solid)(square, solid), (square, solid)(square, solid)(square, solid) (1991)].
    Type of Medium: Electronic Resource
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  • 9
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 32 (1991), S. 3094-3100 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: New properties on parabosonic and parafermionic Cusson's realizations of the Green's Anzätze are first obtained. Then paraproperties are shown to have a specific interest for our real world, where bosons and fermions have to be superposed if Nature is supersymmetric, these results being obtained on supersymmetric harmonic oscillators. In particular, from the Green–Cusson Ansätze, we construct a class of supersymmetric Hamiltonians that are more general than the ones issued from standard or spin–orbit coupling considerations. We explicitly consider the simplest (previously unknown) super-Hamiltonian constructed from paraproperties in quantum mechanics and establish its invariance Lie superalgebra.
    Type of Medium: Electronic Resource
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  • 10
    Electronic Resource
    Electronic Resource
    Amsterdam : Elsevier
    Physics Letters A 178 (1993), S. 43-46 
    ISSN: 0375-9601
    Source: Elsevier Journal Backfiles on ScienceDirect 1907 - 2002
    Topics: Physics
    Type of Medium: Electronic Resource
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